Unwanted Wave-like Shades in the Background as the Object Moves
Without knowing in which format you are rendering and what quality settings you use it's hard to tell the exact reason, but these are no shades depending on the animation itself or the render settings, I guess. These effects are called Banding, Colour Banding or Posterization and can appear in all kinds of software or images. It's usually a problem of insufficient bit depth to display smooth color transitions.  The reason for the low quality can be high compression in image or video formats for example.
Short articles on these topics:
https://en.wikipedia.org/wiki/Colour_banding
https://en.wikipedia.org/wiki/Posterization